How to properly describe work history on a CV for roles where the work was for a seperate company than the employing one

Question

I've had a few roles in the past that were structured like so:

1. The government funded a public university to work on industry projects/research
2. The university hired me over multiple contracts as a developer to work on such projects, and were the ones that signed my paychecks
3. Apart from the paperwork of accepting the position and submitting time sheets, I had no other contact or oversight with the university (except for one role, in which a professor was also directly involved in the project); I reported to management at the industry companies, was given tasks directly by management, worked at their offices, attended business meetings with their clients, and so forth.

Essentially, I was working for the industry companies, while being paid by the university.

Previously I have in my CV's work history section recorded such positions like thus:

[Industry company name] - [period of employment]
[one-line summary of company]
Software Engineer (Subcontracted via [university name])
[paragraph of responsibilities, achievements, work performed, etc]

However, I am not sure if 'subcontracted' is the right term to explain the relationship between myself, the company and the university, and whether it is appropriate to have the company or the university as the heading of each such position.

I feel like if I put the university as the heading (and replace 'subcontracted via [university]' to 'subcontracted to [company]'), it understates the amount of hands-on experience working on industry projects I have, suggests I have more experience working in a university than I do, and also ends up repeating the company summary multiple times. I could resolve the latter by putting all the projects into one section, but I've had other roles in between those, so the chronology gets messed up.

I'm worried though that if I leave it with the industry company as the heading, it will misrepresent my actual employment history, since I've only worked on projects with those companies, rather than be directly employed by them.

Is there a better term than 'subcontract' to describe the relationship between myself, the companies and the university, and what might be a good way to concisely format such roles that accurately explains both that the employer (IE the one signing the paychecks) was the university, and that the work itself was conducted for and with the companies, with essentially no oversight from the employer?

Answer 1

You need to list your actual employer, the university. If someone wants to do a background check based on your resume, they'd need to contact the university to confirm your dates of employment. If they contact the industry company, they'll say they have no record of ever employing you since, well, they didn't employ you.

You're in basically the same position as anyone that works for a contracting company. Your employer is the contracting company but you're actually doing work for various client companies. Generally that looks something like

Contracting Company - Software Engineer - Start - End
  Client Company  Start - End
    Polished widgets using Widget Polisher 2000

  Client Company 2 Start - End
    Stamped widgets using Widget Stamper 2005 and polished using Widget Polisher 2010

That makes it clear that you were working for the contracting company (or in your case the university) when background checks happen but shows what you were actually working on at the different client companies.

Answer 2

You were employed by the university. The fact that the work you performed was for another company that contracted with the university for this work is immaterial.